Actual source code: rosw.c
petsc-3.7.5 2017-01-01
1: /*
2: Code for timestepping with Rosenbrock W methods
4: Notes:
5: The general system is written as
7: F(t,U,Udot) = G(t,U)
9: where F represents the stiff part of the physics and G represents the non-stiff part.
10: This method is designed to be linearly implicit on F and can use an approximate and lagged Jacobian.
12: */
13: #include <petsc/private/tsimpl.h> /*I "petscts.h" I*/
14: #include <petscdm.h>
16: #include <petsc/private/kernels/blockinvert.h>
18: static TSRosWType TSRosWDefault = TSROSWRA34PW2;
19: static PetscBool TSRosWRegisterAllCalled;
20: static PetscBool TSRosWPackageInitialized;
22: typedef struct _RosWTableau *RosWTableau;
23: struct _RosWTableau {
24: char *name;
25: PetscInt order; /* Classical approximation order of the method */
26: PetscInt s; /* Number of stages */
27: PetscInt pinterp; /* Interpolation order */
28: PetscReal *A; /* Propagation table, strictly lower triangular */
29: PetscReal *Gamma; /* Stage table, lower triangular with nonzero diagonal */
30: PetscBool *GammaZeroDiag; /* Diagonal entries that are zero in stage table Gamma, vector indicating explicit statages */
31: PetscReal *GammaExplicitCorr; /* Coefficients for correction terms needed for explicit stages in transformed variables*/
32: PetscReal *b; /* Step completion table */
33: PetscReal *bembed; /* Step completion table for embedded method of order one less */
34: PetscReal *ASum; /* Row sum of A */
35: PetscReal *GammaSum; /* Row sum of Gamma, only needed for non-autonomous systems */
36: PetscReal *At; /* Propagation table in transformed variables */
37: PetscReal *bt; /* Step completion table in transformed variables */
38: PetscReal *bembedt; /* Step completion table of order one less in transformed variables */
39: PetscReal *GammaInv; /* Inverse of Gamma, used for transformed variables */
40: PetscReal ccfl; /* Placeholder for CFL coefficient relative to forward Euler */
41: PetscReal *binterpt; /* Dense output formula */
42: };
43: typedef struct _RosWTableauLink *RosWTableauLink;
44: struct _RosWTableauLink {
45: struct _RosWTableau tab;
46: RosWTableauLink next;
47: };
48: static RosWTableauLink RosWTableauList;
50: typedef struct {
51: RosWTableau tableau;
52: Vec *Y; /* States computed during the step, used to complete the step */
53: Vec Ydot; /* Work vector holding Ydot during residual evaluation */
54: Vec Ystage; /* Work vector for the state value at each stage */
55: Vec Zdot; /* Ydot = Zdot + shift*Y */
56: Vec Zstage; /* Y = Zstage + Y */
57: Vec vec_sol_prev; /* Solution from the previous step (used for interpolation and rollback)*/
58: PetscScalar *work; /* Scalar work space of length number of stages, used to prepare VecMAXPY() */
59: PetscReal scoeff; /* shift = scoeff/dt */
60: PetscReal stage_time;
61: PetscReal stage_explicit; /* Flag indicates that the current stage is explicit */
62: PetscBool recompute_jacobian; /* Recompute the Jacobian at each stage, default is to freeze the Jacobian at the start of each step */
63: TSStepStatus status;
64: } TS_RosW;
66: /*MC
67: TSROSWTHETA1 - One stage first order L-stable Rosenbrock-W scheme (aka theta method).
69: Only an approximate Jacobian is needed.
71: Level: intermediate
73: .seealso: TSROSW
74: M*/
76: /*MC
77: TSROSWTHETA2 - One stage second order A-stable Rosenbrock-W scheme (aka theta method).
79: Only an approximate Jacobian is needed.
81: Level: intermediate
83: .seealso: TSROSW
84: M*/
86: /*MC
87: TSROSW2M - Two stage second order L-stable Rosenbrock-W scheme.
89: Only an approximate Jacobian is needed. By default, it is only recomputed once per step. This method is a reflection of TSROSW2P.
91: Level: intermediate
93: .seealso: TSROSW
94: M*/
96: /*MC
97: TSROSW2P - Two stage second order L-stable Rosenbrock-W scheme.
99: Only an approximate Jacobian is needed. By default, it is only recomputed once per step. This method is a reflection of TSROSW2M.
101: Level: intermediate
103: .seealso: TSROSW
104: M*/
106: /*MC
107: TSROSWRA3PW - Three stage third order Rosenbrock-W scheme for PDAE of index 1.
109: Only an approximate Jacobian is needed. By default, it is only recomputed once per step.
111: This is strongly A-stable with R(infty) = 0.73. The embedded method of order 2 is strongly A-stable with R(infty) = 0.73.
113: References:
114: . 1. - Rang and Angermann, New Rosenbrock W methods of order 3 for partial differential algebraic equations of index 1, 2005.
116: Level: intermediate
118: .seealso: TSROSW
119: M*/
121: /*MC
122: TSROSWRA34PW2 - Four stage third order L-stable Rosenbrock-W scheme for PDAE of index 1.
124: Only an approximate Jacobian is needed. By default, it is only recomputed once per step.
126: This is strongly A-stable with R(infty) = 0. The embedded method of order 2 is strongly A-stable with R(infty) = 0.48.
128: References:
129: . 1. - Rang and Angermann, New Rosenbrock W methods of order 3 for partial differential algebraic equations of index 1, 2005.
131: Level: intermediate
133: .seealso: TSROSW
134: M*/
136: /*MC
137: TSROSWRODAS3 - Four stage third order L-stable Rosenbrock scheme
139: By default, the Jacobian is only recomputed once per step.
141: Both the third order and embedded second order methods are stiffly accurate and L-stable.
143: References:
144: . 1. - Sandu et al, Benchmarking stiff ODE solvers for atmospheric chemistry problems II, Rosenbrock solvers, 1997.
146: Level: intermediate
148: .seealso: TSROSW, TSROSWSANDU3
149: M*/
151: /*MC
152: TSROSWSANDU3 - Three stage third order L-stable Rosenbrock scheme
154: By default, the Jacobian is only recomputed once per step.
156: The third order method is L-stable, but not stiffly accurate.
157: The second order embedded method is strongly A-stable with R(infty) = 0.5.
158: The internal stages are L-stable.
159: This method is called ROS3 in the paper.
161: References:
162: . 1. - Sandu et al, Benchmarking stiff ODE solvers for atmospheric chemistry problems II, Rosenbrock solvers, 1997.
164: Level: intermediate
166: .seealso: TSROSW, TSROSWRODAS3
167: M*/
169: /*MC
170: TSROSWASSP3P3S1C - A-stable Rosenbrock-W method with SSP explicit part, third order, three stages
172: By default, the Jacobian is only recomputed once per step.
174: A-stable SPP explicit order 3, 3 stages, CFL 1 (eff = 1/3)
176: References:
177: . Emil Constantinescu
179: Level: intermediate
181: .seealso: TSROSW, TSROSWLASSP3P4S2C, TSROSWLLSSP3P4S2C, SSP
182: M*/
184: /*MC
185: TSROSWLASSP3P4S2C - L-stable Rosenbrock-W method with SSP explicit part, third order, four stages
187: By default, the Jacobian is only recomputed once per step.
189: L-stable (A-stable embedded) SPP explicit order 3, 4 stages, CFL 2 (eff = 1/2)
191: References:
192: . Emil Constantinescu
194: Level: intermediate
196: .seealso: TSROSW, TSROSWASSP3P3S1C, TSROSWLLSSP3P4S2C, TSSSP
197: M*/
199: /*MC
200: TSROSWLLSSP3P4S2C - L-stable Rosenbrock-W method with SSP explicit part, third order, four stages
202: By default, the Jacobian is only recomputed once per step.
204: L-stable (L-stable embedded) SPP explicit order 3, 4 stages, CFL 2 (eff = 1/2)
206: References:
207: . Emil Constantinescu
209: Level: intermediate
211: .seealso: TSROSW, TSROSWASSP3P3S1C, TSROSWLASSP3P4S2C, TSSSP
212: M*/
214: /*MC
215: TSROSWGRK4T - four stage, fourth order Rosenbrock (not W) method from Kaps and Rentrop
217: By default, the Jacobian is only recomputed once per step.
219: A(89.3 degrees)-stable, |R(infty)| = 0.454.
221: This method does not provide a dense output formula.
223: References:
224: + 1. - Kaps and Rentrop, Generalized Runge Kutta methods of order four with stepsize control for stiff ordinary differential equations, 1979.
225: - 2. - Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.
227: Hairer's code ros4.f
229: Level: intermediate
231: .seealso: TSROSW, TSROSWSHAMP4, TSROSWVELDD4, TSROSW4L
232: M*/
234: /*MC
235: TSROSWSHAMP4 - four stage, fourth order Rosenbrock (not W) method from Shampine
237: By default, the Jacobian is only recomputed once per step.
239: A-stable, |R(infty)| = 1/3.
241: This method does not provide a dense output formula.
243: References:
244: + 1. - Shampine, Implementation of Rosenbrock methods, 1982.
245: - 2. - Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.
247: Hairer's code ros4.f
249: Level: intermediate
251: .seealso: TSROSW, TSROSWGRK4T, TSROSWVELDD4, TSROSW4L
252: M*/
254: /*MC
255: TSROSWVELDD4 - four stage, fourth order Rosenbrock (not W) method from van Veldhuizen
257: By default, the Jacobian is only recomputed once per step.
259: A(89.5 degrees)-stable, |R(infty)| = 0.24.
261: This method does not provide a dense output formula.
263: References:
264: + 1. - van Veldhuizen, D stability and Kaps Rentrop methods, 1984.
265: - 2. - Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.
267: Hairer's code ros4.f
269: Level: intermediate
271: .seealso: TSROSW, TSROSWGRK4T, TSROSWSHAMP4, TSROSW4L
272: M*/
274: /*MC
275: TSROSW4L - four stage, fourth order Rosenbrock (not W) method
277: By default, the Jacobian is only recomputed once per step.
279: A-stable and L-stable
281: This method does not provide a dense output formula.
283: References:
284: . 1. - Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.
286: Hairer's code ros4.f
288: Level: intermediate
290: .seealso: TSROSW, TSROSWGRK4T, TSROSWSHAMP4, TSROSW4L
291: M*/
295: /*@C
296: TSRosWRegisterAll - Registers all of the Rosenbrock-W methods in TSRosW
298: Not Collective, but should be called by all processes which will need the schemes to be registered
300: Level: advanced
302: .keywords: TS, TSRosW, register, all
304: .seealso: TSRosWRegisterDestroy()
305: @*/
306: PetscErrorCode TSRosWRegisterAll(void)
307: {
311: if (TSRosWRegisterAllCalled) return(0);
312: TSRosWRegisterAllCalled = PETSC_TRUE;
314: {
315: const PetscReal A = 0;
316: const PetscReal Gamma = 1;
317: const PetscReal b = 1;
318: const PetscReal binterpt=1;
320: TSRosWRegister(TSROSWTHETA1,1,1,&A,&Gamma,&b,NULL,1,&binterpt);
321: }
323: {
324: const PetscReal A = 0;
325: const PetscReal Gamma = 0.5;
326: const PetscReal b = 1;
327: const PetscReal binterpt=1;
329: TSRosWRegister(TSROSWTHETA2,2,1,&A,&Gamma,&b,NULL,1,&binterpt);
330: }
332: {
333: /*const PetscReal g = 1. + 1./PetscSqrtReal(2.0); Direct evaluation: 1.707106781186547524401. Used for setting up arrays of values known at compile time below. */
334: const PetscReal
335: A[2][2] = {{0,0}, {1.,0}},
336: Gamma[2][2] = {{1.707106781186547524401,0}, {-2.*1.707106781186547524401,1.707106781186547524401}},
337: b[2] = {0.5,0.5},
338: b1[2] = {1.0,0.0};
339: PetscReal binterpt[2][2];
340: binterpt[0][0] = 1.707106781186547524401 - 1.0;
341: binterpt[1][0] = 2.0 - 1.707106781186547524401;
342: binterpt[0][1] = 1.707106781186547524401 - 1.5;
343: binterpt[1][1] = 1.5 - 1.707106781186547524401;
345: TSRosWRegister(TSROSW2P,2,2,&A[0][0],&Gamma[0][0],b,b1,2,&binterpt[0][0]);
346: }
347: {
348: /*const PetscReal g = 1. - 1./PetscSqrtReal(2.0); Direct evaluation: 0.2928932188134524755992. Used for setting up arrays of values known at compile time below. */
349: const PetscReal
350: A[2][2] = {{0,0}, {1.,0}},
351: Gamma[2][2] = {{0.2928932188134524755992,0}, {-2.*0.2928932188134524755992,0.2928932188134524755992}},
352: b[2] = {0.5,0.5},
353: b1[2] = {1.0,0.0};
354: PetscReal binterpt[2][2];
355: binterpt[0][0] = 0.2928932188134524755992 - 1.0;
356: binterpt[1][0] = 2.0 - 0.2928932188134524755992;
357: binterpt[0][1] = 0.2928932188134524755992 - 1.5;
358: binterpt[1][1] = 1.5 - 0.2928932188134524755992;
360: TSRosWRegister(TSROSW2M,2,2,&A[0][0],&Gamma[0][0],b,b1,2,&binterpt[0][0]);
361: }
362: {
363: /*const PetscReal g = 7.8867513459481287e-01; Directly written in-place below */
364: PetscReal binterpt[3][2];
365: const PetscReal
366: A[3][3] = {{0,0,0},
367: {1.5773502691896257e+00,0,0},
368: {0.5,0,0}},
369: Gamma[3][3] = {{7.8867513459481287e-01,0,0},
370: {-1.5773502691896257e+00,7.8867513459481287e-01,0},
371: {-6.7075317547305480e-01,-1.7075317547305482e-01,7.8867513459481287e-01}},
372: b[3] = {1.0566243270259355e-01,4.9038105676657971e-02,8.4529946162074843e-01},
373: b2[3] = {-1.7863279495408180e-01,1./3.,8.4529946162074843e-01};
375: binterpt[0][0] = -0.8094010767585034;
376: binterpt[1][0] = -0.5;
377: binterpt[2][0] = 2.3094010767585034;
378: binterpt[0][1] = 0.9641016151377548;
379: binterpt[1][1] = 0.5;
380: binterpt[2][1] = -1.4641016151377548;
382: TSRosWRegister(TSROSWRA3PW,3,3,&A[0][0],&Gamma[0][0],b,b2,2,&binterpt[0][0]);
383: }
384: {
385: PetscReal binterpt[4][3];
386: /*const PetscReal g = 4.3586652150845900e-01; Directly written in-place below */
387: const PetscReal
388: A[4][4] = {{0,0,0,0},
389: {8.7173304301691801e-01,0,0,0},
390: {8.4457060015369423e-01,-1.1299064236484185e-01,0,0},
391: {0,0,1.,0}},
392: Gamma[4][4] = {{4.3586652150845900e-01,0,0,0},
393: {-8.7173304301691801e-01,4.3586652150845900e-01,0,0},
394: {-9.0338057013044082e-01,5.4180672388095326e-02,4.3586652150845900e-01,0},
395: {2.4212380706095346e-01,-1.2232505839045147e+00,5.4526025533510214e-01,4.3586652150845900e-01}},
396: b[4] = {2.4212380706095346e-01,-1.2232505839045147e+00,1.5452602553351020e+00,4.3586652150845900e-01},
397: b2[4] = {3.7810903145819369e-01,-9.6042292212423178e-02,5.0000000000000000e-01,2.1793326075422950e-01};
399: binterpt[0][0]=1.0564298455794094;
400: binterpt[1][0]=2.296429974281067;
401: binterpt[2][0]=-1.307599564525376;
402: binterpt[3][0]=-1.045260255335102;
403: binterpt[0][1]=-1.3864882699759573;
404: binterpt[1][1]=-8.262611700275677;
405: binterpt[2][1]=7.250979895056055;
406: binterpt[3][1]=2.398120075195581;
407: binterpt[0][2]=0.5721822314575016;
408: binterpt[1][2]=4.742931142090097;
409: binterpt[2][2]=-4.398120075195578;
410: binterpt[3][2]=-0.9169932983520199;
412: TSRosWRegister(TSROSWRA34PW2,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
413: }
414: {
415: /* const PetscReal g = 0.5; Directly written in-place below */
416: const PetscReal
417: A[4][4] = {{0,0,0,0},
418: {0,0,0,0},
419: {1.,0,0,0},
420: {0.75,-0.25,0.5,0}},
421: Gamma[4][4] = {{0.5,0,0,0},
422: {1.,0.5,0,0},
423: {-0.25,-0.25,0.5,0},
424: {1./12,1./12,-2./3,0.5}},
425: b[4] = {5./6,-1./6,-1./6,0.5},
426: b2[4] = {0.75,-0.25,0.5,0};
428: TSRosWRegister(TSROSWRODAS3,3,4,&A[0][0],&Gamma[0][0],b,b2,0,NULL);
429: }
430: {
431: /*const PetscReal g = 0.43586652150845899941601945119356; Directly written in-place below */
432: const PetscReal
433: A[3][3] = {{0,0,0},
434: {0.43586652150845899941601945119356,0,0},
435: {0.43586652150845899941601945119356,0,0}},
436: Gamma[3][3] = {{0.43586652150845899941601945119356,0,0},
437: {-0.19294655696029095575009695436041,0.43586652150845899941601945119356,0},
438: {0,1.74927148125794685173529749738960,0.43586652150845899941601945119356}},
439: b[3] = {-0.75457412385404315829818998646589,1.94100407061964420292840123379419,-0.18642994676560104463021124732829},
440: b2[3] = {-1.53358745784149585370766523913002,2.81745131148625772213931745457622,-0.28386385364476186843165221544619};
442: PetscReal binterpt[3][2];
443: binterpt[0][0] = 3.793692883777660870425141387941;
444: binterpt[1][0] = -2.918692883777660870425141387941;
445: binterpt[2][0] = 0.125;
446: binterpt[0][1] = -0.725741064379812106687651020584;
447: binterpt[1][1] = 0.559074397713145440020984353917;
448: binterpt[2][1] = 0.16666666666666666666666666666667;
450: TSRosWRegister(TSROSWSANDU3,3,3,&A[0][0],&Gamma[0][0],b,b2,2,&binterpt[0][0]);
451: }
452: {
453: /*const PetscReal s3 = PetscSqrtReal(3.),g = (3.0+s3)/6.0;
454: * Direct evaluation: s3 = 1.732050807568877293527;
455: * g = 0.7886751345948128822546;
456: * Values are directly inserted below to ensure availability at compile time (compiler warnings otherwise...) */
457: const PetscReal
458: A[3][3] = {{0,0,0},
459: {1,0,0},
460: {0.25,0.25,0}},
461: Gamma[3][3] = {{0,0,0},
462: {(-3.0-1.732050807568877293527)/6.0,0.7886751345948128822546,0},
463: {(-3.0-1.732050807568877293527)/24.0,(-3.0-1.732050807568877293527)/8.0,0.7886751345948128822546}},
464: b[3] = {1./6.,1./6.,2./3.},
465: b2[3] = {1./4.,1./4.,1./2.};
466: PetscReal binterpt[3][2];
468: binterpt[0][0]=0.089316397477040902157517886164709;
469: binterpt[1][0]=-0.91068360252295909784248211383529;
470: binterpt[2][0]=1.8213672050459181956849642276706;
471: binterpt[0][1]=0.077350269189625764509148780501957;
472: binterpt[1][1]=1.077350269189625764509148780502;
473: binterpt[2][1]=-1.1547005383792515290182975610039;
475: TSRosWRegister(TSROSWASSP3P3S1C,3,3,&A[0][0],&Gamma[0][0],b,b2,2,&binterpt[0][0]);
476: }
478: {
479: const PetscReal
480: A[4][4] = {{0,0,0,0},
481: {1./2.,0,0,0},
482: {1./2.,1./2.,0,0},
483: {1./6.,1./6.,1./6.,0}},
484: Gamma[4][4] = {{1./2.,0,0,0},
485: {0.0,1./4.,0,0},
486: {-2.,-2./3.,2./3.,0},
487: {1./2.,5./36.,-2./9,0}},
488: b[4] = {1./6.,1./6.,1./6.,1./2.},
489: b2[4] = {1./8.,3./4.,1./8.,0};
490: PetscReal binterpt[4][3];
492: binterpt[0][0]=6.25;
493: binterpt[1][0]=-30.25;
494: binterpt[2][0]=1.75;
495: binterpt[3][0]=23.25;
496: binterpt[0][1]=-9.75;
497: binterpt[1][1]=58.75;
498: binterpt[2][1]=-3.25;
499: binterpt[3][1]=-45.75;
500: binterpt[0][2]=3.6666666666666666666666666666667;
501: binterpt[1][2]=-28.333333333333333333333333333333;
502: binterpt[2][2]=1.6666666666666666666666666666667;
503: binterpt[3][2]=23.;
505: TSRosWRegister(TSROSWLASSP3P4S2C,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
506: }
508: {
509: const PetscReal
510: A[4][4] = {{0,0,0,0},
511: {1./2.,0,0,0},
512: {1./2.,1./2.,0,0},
513: {1./6.,1./6.,1./6.,0}},
514: Gamma[4][4] = {{1./2.,0,0,0},
515: {0.0,3./4.,0,0},
516: {-2./3.,-23./9.,2./9.,0},
517: {1./18.,65./108.,-2./27,0}},
518: b[4] = {1./6.,1./6.,1./6.,1./2.},
519: b2[4] = {3./16.,10./16.,3./16.,0};
520: PetscReal binterpt[4][3];
522: binterpt[0][0]=1.6911764705882352941176470588235;
523: binterpt[1][0]=3.6813725490196078431372549019608;
524: binterpt[2][0]=0.23039215686274509803921568627451;
525: binterpt[3][0]=-4.6029411764705882352941176470588;
526: binterpt[0][1]=-0.95588235294117647058823529411765;
527: binterpt[1][1]=-6.2401960784313725490196078431373;
528: binterpt[2][1]=-0.31862745098039215686274509803922;
529: binterpt[3][1]=7.5147058823529411764705882352941;
530: binterpt[0][2]=-0.56862745098039215686274509803922;
531: binterpt[1][2]=2.7254901960784313725490196078431;
532: binterpt[2][2]=0.25490196078431372549019607843137;
533: binterpt[3][2]=-2.4117647058823529411764705882353;
535: TSRosWRegister(TSROSWLLSSP3P4S2C,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
536: }
538: {
539: PetscReal A[4][4],Gamma[4][4],b[4],b2[4];
540: PetscReal binterpt[4][3];
542: Gamma[0][0]=0.4358665215084589994160194475295062513822671686978816;
543: Gamma[0][1]=0; Gamma[0][2]=0; Gamma[0][3]=0;
544: Gamma[1][0]=-1.997527830934941248426324674704153457289527280554476;
545: Gamma[1][1]=0.4358665215084589994160194475295062513822671686978816;
546: Gamma[1][2]=0; Gamma[1][3]=0;
547: Gamma[2][0]=-1.007948511795029620852002345345404191008352770119903;
548: Gamma[2][1]=-0.004648958462629345562774289390054679806993396798458131;
549: Gamma[2][2]=0.4358665215084589994160194475295062513822671686978816;
550: Gamma[2][3]=0;
551: Gamma[3][0]=-0.6685429734233467180451604600279552604364311322650783;
552: Gamma[3][1]=0.6056625986449338476089525334450053439525178740492984;
553: Gamma[3][2]=-0.9717899277217721234705114616271378792182450260943198;
554: Gamma[3][3]=0;
556: A[0][0]=0; A[0][1]=0; A[0][2]=0; A[0][3]=0;
557: A[1][0]=0.8717330430169179988320388950590125027645343373957631;
558: A[1][1]=0; A[1][2]=0; A[1][3]=0;
559: A[2][0]=0.5275890119763004115618079766722914408876108660811028;
560: A[2][1]=0.07241098802369958843819203208518599088698057726988732;
561: A[2][2]=0; A[2][3]=0;
562: A[3][0]=0.3990960076760701320627260685975778145384666450351314;
563: A[3][1]=-0.4375576546135194437228463747348862825846903771419953;
564: A[3][2]=1.038461646937449311660120300601880176655352737312713;
565: A[3][3]=0;
567: b[0]=0.1876410243467238251612921333138006734899663569186926;
568: b[1]=-0.5952974735769549480478230473706443582188442040780541;
569: b[2]=0.9717899277217721234705114616271378792182450260943198;
570: b[3]=0.4358665215084589994160194475295062513822671686978816;
572: b2[0]=0.2147402862233891404862383521089097657790734483804460;
573: b2[1]=-0.4851622638849390928209050538171743017757490232519684;
574: b2[2]=0.8687250025203875511662123688667549217531982787600080;
575: b2[3]=0.4016969751411624011684543450940068201770721128357014;
577: binterpt[0][0]=2.2565812720167954547104627844105;
578: binterpt[1][0]=1.349166413351089573796243820819;
579: binterpt[2][0]=-2.4695174540533503758652847586647;
580: binterpt[3][0]=-0.13623023131453465264142184656474;
581: binterpt[0][1]=-3.0826699111559187902922463354557;
582: binterpt[1][1]=-2.4689115685996042534544925650515;
583: binterpt[2][1]=5.7428279814696677152129332773553;
584: binterpt[3][1]=-0.19124650171414467146619437684812;
585: binterpt[0][2]=1.0137296634858471607430756831148;
586: binterpt[1][2]=0.52444768167155973161042570784064;
587: binterpt[2][2]=-2.3015205996945452158771370439586;
588: binterpt[3][2]=0.76334325453713832352363565300308;
590: TSRosWRegister(TSROSWARK3,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
591: }
592: TSRosWRegisterRos4(TSROSWGRK4T,0.231,PETSC_DEFAULT,PETSC_DEFAULT,0,-0.1282612945269037e+01);
593: TSRosWRegisterRos4(TSROSWSHAMP4,0.5,PETSC_DEFAULT,PETSC_DEFAULT,0,125./108.);
594: TSRosWRegisterRos4(TSROSWVELDD4,0.22570811482256823492,PETSC_DEFAULT,PETSC_DEFAULT,0,-1.355958941201148);
595: TSRosWRegisterRos4(TSROSW4L,0.57282,PETSC_DEFAULT,PETSC_DEFAULT,0,-1.093502252409163);
596: return(0);
597: }
603: /*@C
604: TSRosWRegisterDestroy - Frees the list of schemes that were registered by TSRosWRegister().
606: Not Collective
608: Level: advanced
610: .keywords: TSRosW, register, destroy
611: .seealso: TSRosWRegister(), TSRosWRegisterAll()
612: @*/
613: PetscErrorCode TSRosWRegisterDestroy(void)
614: {
615: PetscErrorCode ierr;
616: RosWTableauLink link;
619: while ((link = RosWTableauList)) {
620: RosWTableau t = &link->tab;
621: RosWTableauList = link->next;
622: PetscFree5(t->A,t->Gamma,t->b,t->ASum,t->GammaSum);
623: PetscFree5(t->At,t->bt,t->GammaInv,t->GammaZeroDiag,t->GammaExplicitCorr);
624: PetscFree2(t->bembed,t->bembedt);
625: PetscFree(t->binterpt);
626: PetscFree(t->name);
627: PetscFree(link);
628: }
629: TSRosWRegisterAllCalled = PETSC_FALSE;
630: return(0);
631: }
635: /*@C
636: TSRosWInitializePackage - This function initializes everything in the TSRosW package. It is called
637: from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to TSCreate_RosW()
638: when using static libraries.
640: Level: developer
642: .keywords: TS, TSRosW, initialize, package
643: .seealso: PetscInitialize()
644: @*/
645: PetscErrorCode TSRosWInitializePackage(void)
646: {
650: if (TSRosWPackageInitialized) return(0);
651: TSRosWPackageInitialized = PETSC_TRUE;
652: TSRosWRegisterAll();
653: PetscRegisterFinalize(TSRosWFinalizePackage);
654: return(0);
655: }
659: /*@C
660: TSRosWFinalizePackage - This function destroys everything in the TSRosW package. It is
661: called from PetscFinalize().
663: Level: developer
665: .keywords: Petsc, destroy, package
666: .seealso: PetscFinalize()
667: @*/
668: PetscErrorCode TSRosWFinalizePackage(void)
669: {
673: TSRosWPackageInitialized = PETSC_FALSE;
674: TSRosWRegisterDestroy();
675: return(0);
676: }
680: /*@C
681: TSRosWRegister - register a Rosenbrock W scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation
683: Not Collective, but the same schemes should be registered on all processes on which they will be used
685: Input Parameters:
686: + name - identifier for method
687: . order - approximation order of method
688: . s - number of stages, this is the dimension of the matrices below
689: . A - Table of propagated stage coefficients (dimension s*s, row-major), strictly lower triangular
690: . Gamma - Table of coefficients in implicit stage equations (dimension s*s, row-major), lower triangular with nonzero diagonal
691: . b - Step completion table (dimension s)
692: . bembed - Step completion table for a scheme of order one less (dimension s, NULL if no embedded scheme is available)
693: . pinterp - Order of the interpolation scheme, equal to the number of columns of binterpt
694: - binterpt - Coefficients of the interpolation formula (dimension s*pinterp)
696: Notes:
697: Several Rosenbrock W methods are provided, this function is only needed to create new methods.
699: Level: advanced
701: .keywords: TS, register
703: .seealso: TSRosW
704: @*/
705: PetscErrorCode TSRosWRegister(TSRosWType name,PetscInt order,PetscInt s,const PetscReal A[],const PetscReal Gamma[],const PetscReal b[],const PetscReal bembed[],
706: PetscInt pinterp,const PetscReal binterpt[])
707: {
708: PetscErrorCode ierr;
709: RosWTableauLink link;
710: RosWTableau t;
711: PetscInt i,j,k;
712: PetscScalar *GammaInv;
721: PetscCalloc1(1,&link);
722: t = &link->tab;
723: PetscStrallocpy(name,&t->name);
724: t->order = order;
725: t->s = s;
726: PetscMalloc5(s*s,&t->A,s*s,&t->Gamma,s,&t->b,s,&t->ASum,s,&t->GammaSum);
727: PetscMalloc5(s*s,&t->At,s,&t->bt,s*s,&t->GammaInv,s,&t->GammaZeroDiag,s*s,&t->GammaExplicitCorr);
728: PetscMemcpy(t->A,A,s*s*sizeof(A[0]));
729: PetscMemcpy(t->Gamma,Gamma,s*s*sizeof(Gamma[0]));
730: PetscMemcpy(t->GammaExplicitCorr,Gamma,s*s*sizeof(Gamma[0]));
731: PetscMemcpy(t->b,b,s*sizeof(b[0]));
732: if (bembed) {
733: PetscMalloc2(s,&t->bembed,s,&t->bembedt);
734: PetscMemcpy(t->bembed,bembed,s*sizeof(bembed[0]));
735: }
736: for (i=0; i<s; i++) {
737: t->ASum[i] = 0;
738: t->GammaSum[i] = 0;
739: for (j=0; j<s; j++) {
740: t->ASum[i] += A[i*s+j];
741: t->GammaSum[i] += Gamma[i*s+j];
742: }
743: }
744: PetscMalloc1(s*s,&GammaInv); /* Need to use Scalar for inverse, then convert back to Real */
745: for (i=0; i<s*s; i++) GammaInv[i] = Gamma[i];
746: for (i=0; i<s; i++) {
747: if (Gamma[i*s+i] == 0.0) {
748: GammaInv[i*s+i] = 1.0;
749: t->GammaZeroDiag[i] = PETSC_TRUE;
750: } else {
751: t->GammaZeroDiag[i] = PETSC_FALSE;
752: }
753: }
755: switch (s) {
756: case 1: GammaInv[0] = 1./GammaInv[0]; break;
757: case 2: PetscKernel_A_gets_inverse_A_2(GammaInv,0,PETSC_FALSE,NULL); break;
758: case 3: PetscKernel_A_gets_inverse_A_3(GammaInv,0,PETSC_FALSE,NULL); break;
759: case 4: PetscKernel_A_gets_inverse_A_4(GammaInv,0,PETSC_FALSE,NULL); break;
760: case 5: {
761: PetscInt ipvt5[5];
762: MatScalar work5[5*5];
763: PetscKernel_A_gets_inverse_A_5(GammaInv,ipvt5,work5,0,PETSC_FALSE,NULL); break;
764: }
765: case 6: PetscKernel_A_gets_inverse_A_6(GammaInv,0,PETSC_FALSE,NULL); break;
766: case 7: PetscKernel_A_gets_inverse_A_7(GammaInv,0,PETSC_FALSE,NULL); break;
767: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for %D stages",s);
768: }
769: for (i=0; i<s*s; i++) t->GammaInv[i] = PetscRealPart(GammaInv[i]);
770: PetscFree(GammaInv);
772: for (i=0; i<s; i++) {
773: for (k=0; k<i+1; k++) {
774: t->GammaExplicitCorr[i*s+k]=(t->GammaExplicitCorr[i*s+k])*(t->GammaInv[k*s+k]);
775: for (j=k+1; j<i+1; j++) {
776: t->GammaExplicitCorr[i*s+k]+=(t->GammaExplicitCorr[i*s+j])*(t->GammaInv[j*s+k]);
777: }
778: }
779: }
781: for (i=0; i<s; i++) {
782: for (j=0; j<s; j++) {
783: t->At[i*s+j] = 0;
784: for (k=0; k<s; k++) {
785: t->At[i*s+j] += t->A[i*s+k] * t->GammaInv[k*s+j];
786: }
787: }
788: t->bt[i] = 0;
789: for (j=0; j<s; j++) {
790: t->bt[i] += t->b[j] * t->GammaInv[j*s+i];
791: }
792: if (bembed) {
793: t->bembedt[i] = 0;
794: for (j=0; j<s; j++) {
795: t->bembedt[i] += t->bembed[j] * t->GammaInv[j*s+i];
796: }
797: }
798: }
799: t->ccfl = 1.0; /* Fix this */
801: t->pinterp = pinterp;
802: PetscMalloc1(s*pinterp,&t->binterpt);
803: PetscMemcpy(t->binterpt,binterpt,s*pinterp*sizeof(binterpt[0]));
804: link->next = RosWTableauList;
805: RosWTableauList = link;
806: return(0);
807: }
811: /*@C
812: TSRosWRegisterRos4 - register a fourth order Rosenbrock scheme by providing paramter choices
814: Not Collective, but the same schemes should be registered on all processes on which they will be used
816: Input Parameters:
817: + name - identifier for method
818: . gamma - leading coefficient (diagonal entry)
819: . a2 - design parameter, see Table 7.2 of Hairer&Wanner
820: . a3 - design parameter or PETSC_DEFAULT to satisfy one of the order five conditions (Eq 7.22)
821: . b3 - design parameter, see Table 7.2 of Hairer&Wanner
822: . beta43 - design parameter or PETSC_DEFAULT to use Equation 7.21 of Hairer&Wanner
823: . e4 - design parameter for embedded method, see coefficient E4 in ros4.f code from Hairer
825: Notes:
826: This routine encodes the design of fourth order Rosenbrock methods as described in Hairer and Wanner volume 2.
827: It is used here to implement several methods from the book and can be used to experiment with new methods.
828: It was written this way instead of by copying coefficients in order to provide better than double precision satisfaction of the order conditions.
830: Level: developer
832: .keywords: TS, register
834: .seealso: TSRosW, TSRosWRegister()
835: @*/
836: PetscErrorCode TSRosWRegisterRos4(TSRosWType name,PetscReal gamma,PetscReal a2,PetscReal a3,PetscReal b3,PetscReal e4)
837: {
839: /* Declare numeric constants so they can be quad precision without being truncated at double */
840: const PetscReal one = 1,two = 2,three = 3,four = 4,five = 5,six = 6,eight = 8,twelve = 12,twenty = 20,twentyfour = 24,
841: p32 = one/six - gamma + gamma*gamma,
842: p42 = one/eight - gamma/three,
843: p43 = one/twelve - gamma/three,
844: p44 = one/twentyfour - gamma/two + three/two*gamma*gamma - gamma*gamma*gamma,
845: p56 = one/twenty - gamma/four;
846: PetscReal a4,a32,a42,a43,b1,b2,b4,beta2p,beta3p,beta4p,beta32,beta42,beta43,beta32beta2p,beta4jbetajp;
847: PetscReal A[4][4],Gamma[4][4],b[4],bm[4];
848: PetscScalar M[3][3],rhs[3];
851: /* Step 1: choose Gamma (input) */
852: /* Step 2: choose a2,a3,a4; b1,b2,b3,b4 to satisfy order conditions */
853: if (a3 == PETSC_DEFAULT) a3 = (one/five - a2/four)/(one/four - a2/three); /* Eq 7.22 */
854: a4 = a3; /* consequence of 7.20 */
856: /* Solve order conditions 7.15a, 7.15c, 7.15e */
857: M[0][0] = one; M[0][1] = one; M[0][2] = one; /* 7.15a */
858: M[1][0] = 0.0; M[1][1] = a2*a2; M[1][2] = a4*a4; /* 7.15c */
859: M[2][0] = 0.0; M[2][1] = a2*a2*a2; M[2][2] = a4*a4*a4; /* 7.15e */
860: rhs[0] = one - b3;
861: rhs[1] = one/three - a3*a3*b3;
862: rhs[2] = one/four - a3*a3*a3*b3;
863: PetscKernel_A_gets_inverse_A_3(&M[0][0],0,PETSC_FALSE,NULL);
864: b1 = PetscRealPart(M[0][0]*rhs[0] + M[0][1]*rhs[1] + M[0][2]*rhs[2]);
865: b2 = PetscRealPart(M[1][0]*rhs[0] + M[1][1]*rhs[1] + M[1][2]*rhs[2]);
866: b4 = PetscRealPart(M[2][0]*rhs[0] + M[2][1]*rhs[1] + M[2][2]*rhs[2]);
868: /* Step 3 */
869: beta43 = (p56 - a2*p43) / (b4*a3*a3*(a3 - a2)); /* 7.21 */
870: beta32beta2p = p44 / (b4*beta43); /* 7.15h */
871: beta4jbetajp = (p32 - b3*beta32beta2p) / b4;
872: M[0][0] = b2; M[0][1] = b3; M[0][2] = b4;
873: M[1][0] = a4*a4*beta32beta2p-a3*a3*beta4jbetajp; M[1][1] = a2*a2*beta4jbetajp; M[1][2] = -a2*a2*beta32beta2p;
874: M[2][0] = b4*beta43*a3*a3-p43; M[2][1] = -b4*beta43*a2*a2; M[2][2] = 0;
875: rhs[0] = one/two - gamma; rhs[1] = 0; rhs[2] = -a2*a2*p32;
876: PetscKernel_A_gets_inverse_A_3(&M[0][0],0,PETSC_FALSE,NULL);
877: beta2p = PetscRealPart(M[0][0]*rhs[0] + M[0][1]*rhs[1] + M[0][2]*rhs[2]);
878: beta3p = PetscRealPart(M[1][0]*rhs[0] + M[1][1]*rhs[1] + M[1][2]*rhs[2]);
879: beta4p = PetscRealPart(M[2][0]*rhs[0] + M[2][1]*rhs[1] + M[2][2]*rhs[2]);
881: /* Step 4: back-substitute */
882: beta32 = beta32beta2p / beta2p;
883: beta42 = (beta4jbetajp - beta43*beta3p) / beta2p;
885: /* Step 5: 7.15f and 7.20, then 7.16 */
886: a43 = 0;
887: a32 = p42 / (b3*a3*beta2p + b4*a4*beta2p);
888: a42 = a32;
890: A[0][0] = 0; A[0][1] = 0; A[0][2] = 0; A[0][3] = 0;
891: A[1][0] = a2; A[1][1] = 0; A[1][2] = 0; A[1][3] = 0;
892: A[2][0] = a3-a32; A[2][1] = a32; A[2][2] = 0; A[2][3] = 0;
893: A[3][0] = a4-a43-a42; A[3][1] = a42; A[3][2] = a43; A[3][3] = 0;
894: Gamma[0][0] = gamma; Gamma[0][1] = 0; Gamma[0][2] = 0; Gamma[0][3] = 0;
895: Gamma[1][0] = beta2p-A[1][0]; Gamma[1][1] = gamma; Gamma[1][2] = 0; Gamma[1][3] = 0;
896: Gamma[2][0] = beta3p-beta32-A[2][0]; Gamma[2][1] = beta32-A[2][1]; Gamma[2][2] = gamma; Gamma[2][3] = 0;
897: Gamma[3][0] = beta4p-beta42-beta43-A[3][0]; Gamma[3][1] = beta42-A[3][1]; Gamma[3][2] = beta43-A[3][2]; Gamma[3][3] = gamma;
898: b[0] = b1; b[1] = b2; b[2] = b3; b[3] = b4;
900: /* Construct embedded formula using given e4. We are solving Equation 7.18. */
901: bm[3] = b[3] - e4*gamma; /* using definition of E4 */
902: bm[2] = (p32 - beta4jbetajp*bm[3]) / (beta32*beta2p); /* fourth row of 7.18 */
903: bm[1] = (one/two - gamma - beta3p*bm[2] - beta4p*bm[3]) / beta2p; /* second row */
904: bm[0] = one - bm[1] - bm[2] - bm[3]; /* first row */
906: {
907: const PetscReal misfit = a2*a2*bm[1] + a3*a3*bm[2] + a4*a4*bm[3] - one/three;
908: if (PetscAbs(misfit) > PETSC_SMALL) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Assumptions violated, could not construct a third order embedded method");
909: }
910: TSRosWRegister(name,4,4,&A[0][0],&Gamma[0][0],b,bm,0,NULL);
911: return(0);
912: }
916: /*
917: The step completion formula is
919: x1 = x0 + b^T Y
921: where Y is the multi-vector of stages corrections. This function can be called before or after ts->vec_sol has been
922: updated. Suppose we have a completion formula b and an embedded formula be of different order. We can write
924: x1e = x0 + be^T Y
925: = x1 - b^T Y + be^T Y
926: = x1 + (be - b)^T Y
928: so we can evaluate the method of different order even after the step has been optimistically completed.
929: */
930: static PetscErrorCode TSEvaluateStep_RosW(TS ts,PetscInt order,Vec U,PetscBool *done)
931: {
932: TS_RosW *ros = (TS_RosW*)ts->data;
933: RosWTableau tab = ros->tableau;
934: PetscScalar *w = ros->work;
935: PetscInt i;
939: if (order == tab->order) {
940: if (ros->status == TS_STEP_INCOMPLETE) { /* Use standard completion formula */
941: VecCopy(ts->vec_sol,U);
942: for (i=0; i<tab->s; i++) w[i] = tab->bt[i];
943: VecMAXPY(U,tab->s,w,ros->Y);
944: } else {VecCopy(ts->vec_sol,U);}
945: if (done) *done = PETSC_TRUE;
946: return(0);
947: } else if (order == tab->order-1) {
948: if (!tab->bembedt) goto unavailable;
949: if (ros->status == TS_STEP_INCOMPLETE) { /* Use embedded completion formula */
950: VecCopy(ts->vec_sol,U);
951: for (i=0; i<tab->s; i++) w[i] = tab->bembedt[i];
952: VecMAXPY(U,tab->s,w,ros->Y);
953: } else { /* Use rollback-and-recomplete formula (bembedt - bt) */
954: for (i=0; i<tab->s; i++) w[i] = tab->bembedt[i] - tab->bt[i];
955: VecCopy(ts->vec_sol,U);
956: VecMAXPY(U,tab->s,w,ros->Y);
957: }
958: if (done) *done = PETSC_TRUE;
959: return(0);
960: }
961: unavailable:
962: if (done) *done = PETSC_FALSE;
963: else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Rosenbrock-W '%s' of order %D cannot evaluate step at order %D. Consider using -ts_adapt_type none or a different method that has an embedded estimate.",tab->name,tab->order,order);
964: return(0);
965: }
969: static PetscErrorCode TSRollBack_RosW(TS ts)
970: {
971: TS_RosW *ros = (TS_RosW*)ts->data;
975: VecCopy(ros->vec_sol_prev,ts->vec_sol);
976: return(0);
977: }
981: static PetscErrorCode TSStep_RosW(TS ts)
982: {
983: TS_RosW *ros = (TS_RosW*)ts->data;
984: RosWTableau tab = ros->tableau;
985: const PetscInt s = tab->s;
986: const PetscReal *At = tab->At,*Gamma = tab->Gamma,*ASum = tab->ASum,*GammaInv = tab->GammaInv;
987: const PetscReal *GammaExplicitCorr = tab->GammaExplicitCorr;
988: const PetscBool *GammaZeroDiag = tab->GammaZeroDiag;
989: PetscScalar *w = ros->work;
990: Vec *Y = ros->Y,Ydot = ros->Ydot,Zdot = ros->Zdot,Zstage = ros->Zstage;
991: SNES snes;
992: TSAdapt adapt;
993: PetscInt i,j,its,lits;
994: PetscInt rejections = 0;
995: PetscBool stageok,accept = PETSC_TRUE;
996: PetscReal next_time_step = ts->time_step;
997: PetscErrorCode ierr;
1000: if (!ts->steprollback) {
1001: VecCopy(ts->vec_sol,ros->vec_sol_prev);
1002: }
1004: ros->status = TS_STEP_INCOMPLETE;
1005: while (!ts->reason && ros->status != TS_STEP_COMPLETE) {
1006: const PetscReal h = ts->time_step;
1007: for (i=0; i<s; i++) {
1008: ros->stage_time = ts->ptime + h*ASum[i];
1009: TSPreStage(ts,ros->stage_time);
1010: if (GammaZeroDiag[i]) {
1011: ros->stage_explicit = PETSC_TRUE;
1012: ros->scoeff = 1.;
1013: } else {
1014: ros->stage_explicit = PETSC_FALSE;
1015: ros->scoeff = 1./Gamma[i*s+i];
1016: }
1018: VecCopy(ts->vec_sol,Zstage);
1019: for (j=0; j<i; j++) w[j] = At[i*s+j];
1020: VecMAXPY(Zstage,i,w,Y);
1022: for (j=0; j<i; j++) w[j] = 1./h * GammaInv[i*s+j];
1023: VecZeroEntries(Zdot);
1024: VecMAXPY(Zdot,i,w,Y);
1026: /* Initial guess taken from last stage */
1027: VecZeroEntries(Y[i]);
1029: if (!ros->stage_explicit) {
1030: TSGetSNES(ts,&snes);
1031: if (!ros->recompute_jacobian && !i) {
1032: SNESSetLagJacobian(snes,-2); /* Recompute the Jacobian on this solve, but not again */
1033: }
1034: SNESSolve(snes,NULL,Y[i]);
1035: SNESGetIterationNumber(snes,&its);
1036: SNESGetLinearSolveIterations(snes,&lits);
1037: ts->snes_its += its; ts->ksp_its += lits;
1038: } else {
1039: Mat J,Jp;
1040: VecZeroEntries(Ydot); /* Evaluate Y[i]=G(t,Ydot=0,Zstage) */
1041: TSComputeIFunction(ts,ros->stage_time,Zstage,Ydot,Y[i],PETSC_FALSE);
1042: VecScale(Y[i],-1.0);
1043: VecAXPY(Y[i],-1.0,Zdot); /*Y[i] = F(Zstage)-Zdot[=GammaInv*Y]*/
1045: VecZeroEntries(Zstage); /* Zstage = GammaExplicitCorr[i,j] * Y[j] */
1046: for (j=0; j<i; j++) w[j] = GammaExplicitCorr[i*s+j];
1047: VecMAXPY(Zstage,i,w,Y);
1049: /* Y[i] = Y[i] + Jac*Zstage[=Jac*GammaExplicitCorr[i,j] * Y[j]] */
1050: TSGetIJacobian(ts,&J,&Jp,NULL,NULL);
1051: TSComputeIJacobian(ts,ros->stage_time,ts->vec_sol,Ydot,0,J,Jp,PETSC_FALSE);
1052: MatMult(J,Zstage,Zdot);
1053: VecAXPY(Y[i],-1.0,Zdot);
1054: ts->ksp_its += 1;
1056: VecScale(Y[i],h);
1057: }
1058: TSPostStage(ts,ros->stage_time,i,Y);
1059: TSGetAdapt(ts,&adapt);
1060: TSAdaptCheckStage(adapt,ts,ros->stage_time,Y[i],&stageok);
1061: if (!stageok) goto reject_step;
1062: }
1064: ros->status = TS_STEP_INCOMPLETE;
1065: TSEvaluateStep_RosW(ts,tab->order,ts->vec_sol,NULL);
1066: ros->status = TS_STEP_PENDING;
1067: TSGetAdapt(ts,&adapt);
1068: TSAdaptCandidatesClear(adapt);
1069: TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,1.*tab->s,PETSC_TRUE);
1070: TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
1071: ros->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
1072: if (!accept) { /* Roll back the current step */
1073: TSRollBack_RosW(ts);
1074: ts->time_step = next_time_step;
1075: goto reject_step;
1076: }
1078: ts->ptime += ts->time_step;
1079: ts->time_step = next_time_step;
1080: break;
1082: reject_step:
1083: ts->reject++; accept = PETSC_FALSE;
1084: if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
1085: ts->reason = TS_DIVERGED_STEP_REJECTED;
1086: PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
1087: }
1088: }
1089: return(0);
1090: }
1094: static PetscErrorCode TSInterpolate_RosW(TS ts,PetscReal itime,Vec U)
1095: {
1096: TS_RosW *ros = (TS_RosW*)ts->data;
1097: PetscInt s = ros->tableau->s,pinterp = ros->tableau->pinterp,i,j;
1098: PetscReal h;
1099: PetscReal tt,t;
1100: PetscScalar *bt;
1101: const PetscReal *Bt = ros->tableau->binterpt;
1102: PetscErrorCode ierr;
1103: const PetscReal *GammaInv = ros->tableau->GammaInv;
1104: PetscScalar *w = ros->work;
1105: Vec *Y = ros->Y;
1108: if (!Bt) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRosW %s does not have an interpolation formula",ros->tableau->name);
1110: switch (ros->status) {
1111: case TS_STEP_INCOMPLETE:
1112: case TS_STEP_PENDING:
1113: h = ts->time_step;
1114: t = (itime - ts->ptime)/h;
1115: break;
1116: case TS_STEP_COMPLETE:
1117: h = ts->ptime - ts->ptime_prev;
1118: t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
1119: break;
1120: default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
1121: }
1122: PetscMalloc1(s,&bt);
1123: for (i=0; i<s; i++) bt[i] = 0;
1124: for (j=0,tt=t; j<pinterp; j++,tt*=t) {
1125: for (i=0; i<s; i++) {
1126: bt[i] += Bt[i*pinterp+j] * tt;
1127: }
1128: }
1130: /* y(t+tt*h) = y(t) + Sum bt(tt) * GammaInv * Ydot */
1131: /* U <- 0*/
1132: VecZeroEntries(U);
1133: /* U <- Sum bt_i * GammaInv(i,1:i) * Y(1:i) */
1134: for (j=0; j<s; j++) w[j] = 0;
1135: for (j=0; j<s; j++) {
1136: for (i=j; i<s; i++) {
1137: w[j] += bt[i]*GammaInv[i*s+j];
1138: }
1139: }
1140: VecMAXPY(U,i,w,Y);
1141: /* U <- y(t) + U */
1142: VecAXPY(U,1,ros->vec_sol_prev);
1144: PetscFree(bt);
1145: return(0);
1146: }
1148: /*------------------------------------------------------------*/
1152: static PetscErrorCode TSRosWTableauReset(TS ts)
1153: {
1154: TS_RosW *ros = (TS_RosW*)ts->data;
1155: RosWTableau tab = ros->tableau;
1159: if (!tab) return(0);
1160: VecDestroyVecs(tab->s,&ros->Y);
1161: PetscFree(ros->work);
1162: return(0);
1163: }
1167: static PetscErrorCode TSReset_RosW(TS ts)
1168: {
1169: TS_RosW *ros = (TS_RosW*)ts->data;
1173: TSRosWTableauReset(ts);
1174: VecDestroy(&ros->Ydot);
1175: VecDestroy(&ros->Ystage);
1176: VecDestroy(&ros->Zdot);
1177: VecDestroy(&ros->Zstage);
1178: VecDestroy(&ros->vec_sol_prev);
1179: return(0);
1180: }
1184: static PetscErrorCode TSDestroy_RosW(TS ts)
1185: {
1189: TSReset_RosW(ts);
1190: PetscFree(ts->data);
1191: PetscObjectComposeFunction((PetscObject)ts,"TSRosWGetType_C",NULL);
1192: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetType_C",NULL);
1193: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetRecomputeJacobian_C",NULL);
1194: return(0);
1195: }
1200: static PetscErrorCode TSRosWGetVecs(TS ts,DM dm,Vec *Ydot,Vec *Zdot,Vec *Ystage,Vec *Zstage)
1201: {
1202: TS_RosW *rw = (TS_RosW*)ts->data;
1206: if (Ydot) {
1207: if (dm && dm != ts->dm) {
1208: DMGetNamedGlobalVector(dm,"TSRosW_Ydot",Ydot);
1209: } else *Ydot = rw->Ydot;
1210: }
1211: if (Zdot) {
1212: if (dm && dm != ts->dm) {
1213: DMGetNamedGlobalVector(dm,"TSRosW_Zdot",Zdot);
1214: } else *Zdot = rw->Zdot;
1215: }
1216: if (Ystage) {
1217: if (dm && dm != ts->dm) {
1218: DMGetNamedGlobalVector(dm,"TSRosW_Ystage",Ystage);
1219: } else *Ystage = rw->Ystage;
1220: }
1221: if (Zstage) {
1222: if (dm && dm != ts->dm) {
1223: DMGetNamedGlobalVector(dm,"TSRosW_Zstage",Zstage);
1224: } else *Zstage = rw->Zstage;
1225: }
1226: return(0);
1227: }
1232: static PetscErrorCode TSRosWRestoreVecs(TS ts,DM dm,Vec *Ydot,Vec *Zdot, Vec *Ystage, Vec *Zstage)
1233: {
1237: if (Ydot) {
1238: if (dm && dm != ts->dm) {
1239: DMRestoreNamedGlobalVector(dm,"TSRosW_Ydot",Ydot);
1240: }
1241: }
1242: if (Zdot) {
1243: if (dm && dm != ts->dm) {
1244: DMRestoreNamedGlobalVector(dm,"TSRosW_Zdot",Zdot);
1245: }
1246: }
1247: if (Ystage) {
1248: if (dm && dm != ts->dm) {
1249: DMRestoreNamedGlobalVector(dm,"TSRosW_Ystage",Ystage);
1250: }
1251: }
1252: if (Zstage) {
1253: if (dm && dm != ts->dm) {
1254: DMRestoreNamedGlobalVector(dm,"TSRosW_Zstage",Zstage);
1255: }
1256: }
1257: return(0);
1258: }
1262: static PetscErrorCode DMCoarsenHook_TSRosW(DM fine,DM coarse,void *ctx)
1263: {
1265: return(0);
1266: }
1270: static PetscErrorCode DMRestrictHook_TSRosW(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
1271: {
1272: TS ts = (TS)ctx;
1274: Vec Ydot,Zdot,Ystage,Zstage;
1275: Vec Ydotc,Zdotc,Ystagec,Zstagec;
1278: TSRosWGetVecs(ts,fine,&Ydot,&Ystage,&Zdot,&Zstage);
1279: TSRosWGetVecs(ts,coarse,&Ydotc,&Ystagec,&Zdotc,&Zstagec);
1280: MatRestrict(restrct,Ydot,Ydotc);
1281: VecPointwiseMult(Ydotc,rscale,Ydotc);
1282: MatRestrict(restrct,Ystage,Ystagec);
1283: VecPointwiseMult(Ystagec,rscale,Ystagec);
1284: MatRestrict(restrct,Zdot,Zdotc);
1285: VecPointwiseMult(Zdotc,rscale,Zdotc);
1286: MatRestrict(restrct,Zstage,Zstagec);
1287: VecPointwiseMult(Zstagec,rscale,Zstagec);
1288: TSRosWRestoreVecs(ts,fine,&Ydot,&Ystage,&Zdot,&Zstage);
1289: TSRosWRestoreVecs(ts,coarse,&Ydotc,&Ystagec,&Zdotc,&Zstagec);
1290: return(0);
1291: }
1296: static PetscErrorCode DMSubDomainHook_TSRosW(DM fine,DM coarse,void *ctx)
1297: {
1299: return(0);
1300: }
1304: static PetscErrorCode DMSubDomainRestrictHook_TSRosW(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
1305: {
1306: TS ts = (TS)ctx;
1308: Vec Ydot,Zdot,Ystage,Zstage;
1309: Vec Ydots,Zdots,Ystages,Zstages;
1312: TSRosWGetVecs(ts,dm,&Ydot,&Ystage,&Zdot,&Zstage);
1313: TSRosWGetVecs(ts,subdm,&Ydots,&Ystages,&Zdots,&Zstages);
1315: VecScatterBegin(gscat,Ydot,Ydots,INSERT_VALUES,SCATTER_FORWARD);
1316: VecScatterEnd(gscat,Ydot,Ydots,INSERT_VALUES,SCATTER_FORWARD);
1318: VecScatterBegin(gscat,Ystage,Ystages,INSERT_VALUES,SCATTER_FORWARD);
1319: VecScatterEnd(gscat,Ystage,Ystages,INSERT_VALUES,SCATTER_FORWARD);
1321: VecScatterBegin(gscat,Zdot,Zdots,INSERT_VALUES,SCATTER_FORWARD);
1322: VecScatterEnd(gscat,Zdot,Zdots,INSERT_VALUES,SCATTER_FORWARD);
1324: VecScatterBegin(gscat,Zstage,Zstages,INSERT_VALUES,SCATTER_FORWARD);
1325: VecScatterEnd(gscat,Zstage,Zstages,INSERT_VALUES,SCATTER_FORWARD);
1327: TSRosWRestoreVecs(ts,dm,&Ydot,&Ystage,&Zdot,&Zstage);
1328: TSRosWRestoreVecs(ts,subdm,&Ydots,&Ystages,&Zdots,&Zstages);
1329: return(0);
1330: }
1332: /*
1333: This defines the nonlinear equation that is to be solved with SNES
1334: G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
1335: */
1338: static PetscErrorCode SNESTSFormFunction_RosW(SNES snes,Vec U,Vec F,TS ts)
1339: {
1340: TS_RosW *ros = (TS_RosW*)ts->data;
1342: Vec Ydot,Zdot,Ystage,Zstage;
1343: PetscReal shift = ros->scoeff / ts->time_step;
1344: DM dm,dmsave;
1347: SNESGetDM(snes,&dm);
1348: TSRosWGetVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1349: VecWAXPY(Ydot,shift,U,Zdot); /* Ydot = shift*U + Zdot */
1350: VecWAXPY(Ystage,1.0,U,Zstage); /* Ystage = U + Zstage */
1351: dmsave = ts->dm;
1352: ts->dm = dm;
1353: TSComputeIFunction(ts,ros->stage_time,Ystage,Ydot,F,PETSC_FALSE);
1354: ts->dm = dmsave;
1355: TSRosWRestoreVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1356: return(0);
1357: }
1361: static PetscErrorCode SNESTSFormJacobian_RosW(SNES snes,Vec U,Mat A,Mat B,TS ts)
1362: {
1363: TS_RosW *ros = (TS_RosW*)ts->data;
1364: Vec Ydot,Zdot,Ystage,Zstage;
1365: PetscReal shift = ros->scoeff / ts->time_step;
1367: DM dm,dmsave;
1370: /* ros->Ydot and ros->Ystage have already been computed in SNESTSFormFunction_RosW (SNES guarantees this) */
1371: SNESGetDM(snes,&dm);
1372: TSRosWGetVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1373: dmsave = ts->dm;
1374: ts->dm = dm;
1375: TSComputeIJacobian(ts,ros->stage_time,Ystage,Ydot,shift,A,B,PETSC_TRUE);
1376: ts->dm = dmsave;
1377: TSRosWRestoreVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1378: return(0);
1379: }
1383: static PetscErrorCode TSRosWTableauSetUp(TS ts)
1384: {
1385: TS_RosW *ros = (TS_RosW*)ts->data;
1386: RosWTableau tab = ros->tableau;
1390: VecDuplicateVecs(ts->vec_sol,tab->s,&ros->Y);
1391: PetscMalloc1(tab->s,&ros->work);
1392: return(0);
1393: }
1397: static PetscErrorCode TSSetUp_RosW(TS ts)
1398: {
1399: TS_RosW *ros = (TS_RosW*)ts->data;
1401: DM dm;
1402: SNES snes;
1405: TSRosWTableauSetUp(ts);
1406: VecDuplicate(ts->vec_sol,&ros->Ydot);
1407: VecDuplicate(ts->vec_sol,&ros->Ystage);
1408: VecDuplicate(ts->vec_sol,&ros->Zdot);
1409: VecDuplicate(ts->vec_sol,&ros->Zstage);
1410: VecDuplicate(ts->vec_sol,&ros->vec_sol_prev);
1411: TSGetDM(ts,&dm);
1412: if (dm) {
1413: DMCoarsenHookAdd(dm,DMCoarsenHook_TSRosW,DMRestrictHook_TSRosW,ts);
1414: DMSubDomainHookAdd(dm,DMSubDomainHook_TSRosW,DMSubDomainRestrictHook_TSRosW,ts);
1415: }
1416: /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1417: TSGetSNES(ts,&snes);
1418: if (!((PetscObject)snes)->type_name) {
1419: SNESSetType(snes,SNESKSPONLY);
1420: }
1421: return(0);
1422: }
1423: /*------------------------------------------------------------*/
1427: static PetscErrorCode TSSetFromOptions_RosW(PetscOptionItems *PetscOptionsObject,TS ts)
1428: {
1429: TS_RosW *ros = (TS_RosW*)ts->data;
1431: SNES snes;
1434: PetscOptionsHead(PetscOptionsObject,"RosW ODE solver options");
1435: {
1436: RosWTableauLink link;
1437: PetscInt count,choice;
1438: PetscBool flg;
1439: const char **namelist;
1441: for (link=RosWTableauList,count=0; link; link=link->next,count++) ;
1442: PetscMalloc1(count,&namelist);
1443: for (link=RosWTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
1444: PetscOptionsEList("-ts_rosw_type","Family of Rosenbrock-W method","TSRosWSetType",(const char*const*)namelist,count,ros->tableau->name,&choice,&flg);
1445: if (flg) {TSRosWSetType(ts,namelist[choice]);}
1446: PetscFree(namelist);
1448: PetscOptionsBool("-ts_rosw_recompute_jacobian","Recompute the Jacobian at each stage","TSRosWSetRecomputeJacobian",ros->recompute_jacobian,&ros->recompute_jacobian,NULL);
1449: }
1450: PetscOptionsTail();
1451: /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1452: TSGetSNES(ts,&snes);
1453: if (!((PetscObject)snes)->type_name) {
1454: SNESSetType(snes,SNESKSPONLY);
1455: }
1456: return(0);
1457: }
1461: static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[])
1462: {
1464: PetscInt i;
1465: size_t left,count;
1466: char *p;
1469: for (i=0,p=buf,left=len; i<n; i++) {
1470: PetscSNPrintfCount(p,left,fmt,&count,x[i]);
1471: if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer");
1472: left -= count;
1473: p += count;
1474: *p++ = ' ';
1475: }
1476: p[i ? 0 : -1] = 0;
1477: return(0);
1478: }
1482: static PetscErrorCode TSView_RosW(TS ts,PetscViewer viewer)
1483: {
1484: TS_RosW *ros = (TS_RosW*)ts->data;
1485: PetscBool iascii;
1489: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1490: if (iascii) {
1491: RosWTableau tab = ros->tableau;
1492: TSRosWType rostype;
1493: char buf[512];
1494: PetscInt i;
1495: PetscReal abscissa[512];
1496: TSRosWGetType(ts,&rostype);
1497: PetscViewerASCIIPrintf(viewer," Rosenbrock-W %s\n",rostype);
1498: PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->ASum);
1499: PetscViewerASCIIPrintf(viewer," Abscissa of A = %s\n",buf);
1500: for (i=0; i<tab->s; i++) abscissa[i] = tab->ASum[i] + tab->Gamma[i];
1501: PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,abscissa);
1502: PetscViewerASCIIPrintf(viewer," Abscissa of A+Gamma = %s\n",buf);
1503: }
1504: if (ts->adapt) {TSAdaptView(ts->adapt,viewer);}
1505: if (ts->snes) {SNESView(ts->snes,viewer);}
1506: return(0);
1507: }
1511: static PetscErrorCode TSLoad_RosW(TS ts,PetscViewer viewer)
1512: {
1514: SNES snes;
1515: TSAdapt adapt;
1518: TSGetAdapt(ts,&adapt);
1519: TSAdaptLoad(adapt,viewer);
1520: TSGetSNES(ts,&snes);
1521: SNESLoad(snes,viewer);
1522: /* function and Jacobian context for SNES when used with TS is always ts object */
1523: SNESSetFunction(snes,NULL,NULL,ts);
1524: SNESSetJacobian(snes,NULL,NULL,NULL,ts);
1525: return(0);
1526: }
1530: /*@C
1531: TSRosWSetType - Set the type of Rosenbrock-W scheme
1533: Logically collective
1535: Input Parameter:
1536: + ts - timestepping context
1537: - rostype - type of Rosenbrock-W scheme
1539: Level: beginner
1541: .seealso: TSRosWGetType(), TSROSW, TSROSW2M, TSROSW2P, TSROSWRA3PW, TSROSWRA34PW2, TSROSWRODAS3, TSROSWSANDU3, TSROSWASSP3P3S1C, TSROSWLASSP3P4S2C, TSROSWLLSSP3P4S2C, TSROSWARK3
1542: @*/
1543: PetscErrorCode TSRosWSetType(TS ts,TSRosWType rostype)
1544: {
1549: PetscTryMethod(ts,"TSRosWSetType_C",(TS,TSRosWType),(ts,rostype));
1550: return(0);
1551: }
1555: /*@C
1556: TSRosWGetType - Get the type of Rosenbrock-W scheme
1558: Logically collective
1560: Input Parameter:
1561: . ts - timestepping context
1563: Output Parameter:
1564: . rostype - type of Rosenbrock-W scheme
1566: Level: intermediate
1568: .seealso: TSRosWGetType()
1569: @*/
1570: PetscErrorCode TSRosWGetType(TS ts,TSRosWType *rostype)
1571: {
1576: PetscUseMethod(ts,"TSRosWGetType_C",(TS,TSRosWType*),(ts,rostype));
1577: return(0);
1578: }
1582: /*@C
1583: TSRosWSetRecomputeJacobian - Set whether to recompute the Jacobian at each stage. The default is to update the Jacobian once per step.
1585: Logically collective
1587: Input Parameter:
1588: + ts - timestepping context
1589: - flg - PETSC_TRUE to recompute the Jacobian at each stage
1591: Level: intermediate
1593: .seealso: TSRosWGetType()
1594: @*/
1595: PetscErrorCode TSRosWSetRecomputeJacobian(TS ts,PetscBool flg)
1596: {
1601: PetscTryMethod(ts,"TSRosWSetRecomputeJacobian_C",(TS,PetscBool),(ts,flg));
1602: return(0);
1603: }
1607: static PetscErrorCode TSRosWGetType_RosW(TS ts,TSRosWType *rostype)
1608: {
1609: TS_RosW *ros = (TS_RosW*)ts->data;
1612: *rostype = ros->tableau->name;
1613: return(0);
1614: }
1618: static PetscErrorCode TSRosWSetType_RosW(TS ts,TSRosWType rostype)
1619: {
1620: TS_RosW *ros = (TS_RosW*)ts->data;
1621: PetscErrorCode ierr;
1622: PetscBool match;
1623: RosWTableauLink link;
1626: if (ros->tableau) {
1627: PetscStrcmp(ros->tableau->name,rostype,&match);
1628: if (match) return(0);
1629: }
1630: for (link = RosWTableauList; link; link=link->next) {
1631: PetscStrcmp(link->tab.name,rostype,&match);
1632: if (match) {
1633: if (ts->setupcalled) {TSRosWTableauReset(ts);}
1634: ros->tableau = &link->tab;
1635: if (ts->setupcalled) {TSRosWTableauSetUp(ts);}
1636: return(0);
1637: }
1638: }
1639: SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rostype);
1640: return(0);
1641: }
1645: static PetscErrorCode TSRosWSetRecomputeJacobian_RosW(TS ts,PetscBool flg)
1646: {
1647: TS_RosW *ros = (TS_RosW*)ts->data;
1650: ros->recompute_jacobian = flg;
1651: return(0);
1652: }
1655: /* ------------------------------------------------------------ */
1656: /*MC
1657: TSROSW - ODE solver using Rosenbrock-W schemes
1659: These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly
1660: nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part
1661: of the equation using TSSetIFunction() and the non-stiff part with TSSetRHSFunction().
1663: Notes:
1664: This method currently only works with autonomous ODE and DAE.
1666: Consider trying TSARKIMEX if the stiff part is strongly nonlinear.
1668: Developer notes:
1669: Rosenbrock-W methods are typically specified for autonomous ODE
1671: $ udot = f(u)
1673: by the stage equations
1675: $ k_i = h f(u_0 + sum_j alpha_ij k_j) + h J sum_j gamma_ij k_j
1677: and step completion formula
1679: $ u_1 = u_0 + sum_j b_j k_j
1681: with step size h and coefficients alpha_ij, gamma_ij, and b_i. Implementing the method in this form would require f(u)
1682: and the Jacobian J to be available, in addition to the shifted matrix I - h gamma_ii J. Following Hairer and Wanner,
1683: we define new variables for the stage equations
1685: $ y_i = gamma_ij k_j
1687: The k_j can be recovered because Gamma is invertible. Let C be the lower triangular part of Gamma^{-1} and define
1689: $ A = Alpha Gamma^{-1}, bt^T = b^T Gamma^{-1}
1691: to rewrite the method as
1693: $ [M/(h gamma_ii) - J] y_i = f(u_0 + sum_j a_ij y_j) + M sum_j (c_ij/h) y_j
1694: $ u_1 = u_0 + sum_j bt_j y_j
1696: where we have introduced the mass matrix M. Continue by defining
1698: $ ydot_i = 1/(h gamma_ii) y_i - sum_j (c_ij/h) y_j
1700: or, more compactly in tensor notation
1702: $ Ydot = 1/h (Gamma^{-1} \otimes I) Y .
1704: Note that Gamma^{-1} is lower triangular. With this definition of Ydot in terms of known quantities and the current
1705: stage y_i, the stage equations reduce to performing one Newton step (typically with a lagged Jacobian) on the
1706: equation
1708: $ g(u_0 + sum_j a_ij y_j + y_i, ydot_i) = 0
1710: with initial guess y_i = 0.
1712: Level: beginner
1714: .seealso: TSCreate(), TS, TSSetType(), TSRosWSetType(), TSRosWRegister(), TSROSWTHETA1, TSROSWTHETA2, TSROSW2M, TSROSW2P, TSROSWRA3PW, TSROSWRA34PW2, TSROSWRODAS3,
1715: TSROSWSANDU3, TSROSWASSP3P3S1C, TSROSWLASSP3P4S2C, TSROSWLLSSP3P4S2C, TSROSWGRK4T, TSROSWSHAMP4, TSROSWVELDD4, TSROSW4L
1716: M*/
1719: PETSC_EXTERN PetscErrorCode TSCreate_RosW(TS ts)
1720: {
1721: TS_RosW *ros;
1725: TSRosWInitializePackage();
1727: ts->ops->reset = TSReset_RosW;
1728: ts->ops->destroy = TSDestroy_RosW;
1729: ts->ops->view = TSView_RosW;
1730: ts->ops->load = TSLoad_RosW;
1731: ts->ops->setup = TSSetUp_RosW;
1732: ts->ops->step = TSStep_RosW;
1733: ts->ops->interpolate = TSInterpolate_RosW;
1734: ts->ops->evaluatestep = TSEvaluateStep_RosW;
1735: ts->ops->rollback = TSRollBack_RosW;
1736: ts->ops->setfromoptions = TSSetFromOptions_RosW;
1737: ts->ops->snesfunction = SNESTSFormFunction_RosW;
1738: ts->ops->snesjacobian = SNESTSFormJacobian_RosW;
1740: PetscNewLog(ts,&ros);
1741: ts->data = (void*)ros;
1743: PetscObjectComposeFunction((PetscObject)ts,"TSRosWGetType_C",TSRosWGetType_RosW);
1744: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetType_C",TSRosWSetType_RosW);
1745: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetRecomputeJacobian_C",TSRosWSetRecomputeJacobian_RosW);
1747: TSRosWSetType(ts,TSRosWDefault);
1748: return(0);
1749: }